Loop Spaces, Characteristic Classes and Geometric Quantization
Publication year: 2008
ISBN: 978-0-8176-4731-5
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This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Various developments in mathematical physics (e.g., in knot theory, gauge theory, and topological quantum field theory) have led mathematicians and physicists to search for new geometric structures on manifolds and to seek a synthesis of ideas from geometry, topology and category theory. In this spirit, this book develops the differential geometry associated to the topology and obstruction theory of certain fiber bundles (more precisely, associated to grebes). The theory is a 3-dimensional analog of the familiar Kostant--Weil theory of line bundles. In particular the curvature now becomes a 3-form.
Subject: Mathematics and Statistics, Algebra, Category theory, Knot theory, Kähler geometry, curvature, differential geometry, fiber bundles, group cohomology, loop groups, manifold
